KK773 can be split as 773/KK and K73/K7, both of which are a 20 and a 17, and I get 773/KK (make the 2-card hand higher) as the play.
On the other hand, K9963 can be split into K9/963 and 99/K63, both of which are an 18 and a 19, and I get K63/99 (make the 3-card hand higher) as the play.
Also, with K7764, I get K74/76 over 764/K7 (21/fold over 17/17), but with K8865, I get 865/K8 over K65/88 (19/18 over 21/fold), which means "always keep a 21" is not always the correct play.
Here's another one, although I think I understand this one; with KK655, play 655/KK over K65/K5 (as well as K55/66) - this is a 20/fold over a 21/fold. However, with the house's "make two valid hands if possible" rule, this makes a little sense - if the house has AK977, the only way to make two valid hands is A97/K7, which is 17/17, rather then 977/AK, which is fold/21. Two-card dealer hands will tend to be weaker because of it.
This is about right. As a very simple basic strategy, we have the following:
Since the house favors both making two pat hands at all costs as well as favoring the three-card side, it is better for the player to:
* favor the two-card side if a 20 or 21, and
* Balance towards the three card side with 19's and less, except
* foul one side to avoid having two 17s, if the two-card side can be made a 20 or 21, unless the three-card side can be made a full 21.
Interestingly, at the start of the project, (at the "develop the initial house way" point), we didn't know which side to favor or if to favor two weak pat hands versus one monster 21 hand with a foul side, etc., so we requested an initial EV simulation of optimal dealer play to help develop a solid but easy house way. But the mathematician initially decided to assume "favor the two-card side and add rules if needed" because it looked at that time that this was okay, eye-balling it. So, instead of spending extra time and money to perform an initial sim run of the EVs, front-end corners were cut when he calculated the initial game with this assumption. The initial version had such a weak house edge with the "dealer favors two-card" assumption that the initial version of the game had player Pai Gow-like restrictions, and played awkwardly. Players were forced to foul great make-able hands like 776AJ if adding any sort of high-side/low-side rule. When we insisted again on an EV simulation, we found that favoring the dealer's three-card side improved the house edge enough to eliminate all player hand setting restrictions, which was an initial game spec requirement. Game Design Lesson #1-A: do not cut corners on the front end to save math expenses or a little time. Your new game is up against UTH and Freebet and other great games, so it has to be as fine as possible.
While it is better to make one monster hand than two 17's, because of the extra house way clauses and conditions involved, this then would have made the house way tougher to deal for the dealer, and rougher for the player to play against. With re-done initial math, we could shorten the house way to "make two pat hands first, favoring the three-card side when possible [even if two 17's]" - with the math indicating that this was still strong. So....Game Design Lessons #17-C and #17-D: make the house way easy enough to deal by trimming out hand-setting clauses that are tougher to deal, but cost little to remove by knowing how much, and Make the player feels like he has a shot to win by NOT using a tournament player level type of house way.
Can I safely assume this game was first conceived and/or thought of, after you left Galaxy ?
Yes, it was after galaxy, and was thought up by my partner, not me, who a) never worked for Galaxy and, b) is a retired anesthesiologist (and pretty much a life-long recreational casino patron).
GOOD LUCK, looks like a WINNER
Corrected - this works better if you remember to include hands of two pairs where the fifth card is a 10-value
The house advantage when using "perfect" strategy appears to be 3.036%
Note that when two numbers (or "Fold") are separated by a slash, the first is the 3-card hand, and the second is the 2-card hand
If you can make two valid hands:
1. Make a 3-card 21
2. Make a 3-card 20, except that 18/21 comes before 20/19
3. Make a 2-card 21
4. Make a 2-card 20
5. Make a 3-card 19
6. Make a 3-card 18
7. Make a 2-card 19 (although I am not sure this is possible without having a 3-card 18 or a 2-card 20)
8. Make a 2-card 18
9. Make a 17/17 (but see the exceptions)
Make a 21/Fold over 18/17 or 17/18 (or 17/17)
Make a Fold/20 over 18/17 or 17/18 (or 17/17)
Make a Fold/21 over 19/17, 18/18, or 17/19 (or 18/17, 17/18, or 17/17)
17/20 or 19/18 depends on the hand
19/17 or 18/18 depends on the hand
20/17 or 17/20 depends on the hand
20/18 or 17/21 depends on the hand
20/18 or 18/20 depends on the hand
20/19 or 19/20 depends on the hand
If you cannot make two valid hands:
Make the best single hand (if you have a choice, make the 2-card hand better than the 3-card hand)
Make Fold/N over (N+1)/Fold (for example Fold/20 is better than 21/Fold - split KQ655 into 655/KQ rather than K65/Q5)
Fold/17 or 19/Fold depends on the hand
Fold/18 or 20/Fold depends on the hand
The house advantage when using "perfect" strategy appears to be 3.036%
Don, correct at 3% when offering no "BJ-like" bonuses on a player's double 21.
We have three house edge options, which were checked by both Steve How and GLI lab math:
1. It is actually 3.12% (or 1.56% of the two main bets) with no bonus payout; very close, Don.
2. It is 2.03% (or 1% on the two main bets) with the extra half-unit bonus on the two-card bet when holding a double-21 hand. This pays 3:2 if the player's two-card side 21 wins, and pays 1:2 on a two-card side tie.
3. It is 0.94% (or 0.47%) with an extra full unit payout on the two-card bet when holding a double-21 hand. This pays 2:1 on the two-card side win, and 1:1 on a two-card side push.
The double-21 hand occurs 2.1806% of the time, or once in every 47 hands.
We launched the game with a 2% HE (or 1% EoR), with the half-unit bonus.
One guy looked at it and did a suspicious "Mr. BOOKMAN" take on it, straight out of a Seinfeld episode: "I know what you guys are trying to do here with these new games, I tell ya....you're trying to HOODWINK us, you fancy-pants gangsters, I tell ya...snooker us in, aren't cha, aren't cha, aren't cha... ah-HA, I knew it...!" I'm not kidding you, there was this guy was just standing near the table looking at it like it was from Mars....there's always at least one of these conspiracy guys, just no talking to them. Tell them the Element of Return is only 1%, and they say "don't try to snooker me you fancy-pants hoodlum, I know what you're up to, you're trying to make money..." (and while we are just trying to create good new games, I will say: yeah, we are, on the other point, too.) Sheesh....I felt like telling him "here's a C-note for you, now go play some craps...." It was a while since I last heard the word Bamboozle.... If he had said "THIS is how you guys make your money," I would have answered honestly "yes it is...." Kind of like an Anti-shill for the game....
But most were like, "this is fun, a little strategy...the bonus pays on having two 20's or better, I got two 20's....what's that, five to one, that's $50, okay...."
We're hoping for steady, friendly action...
It is 2.03% (or 1% on the two main bets) with the extra half-unit bonus on the two-card bet when holding a double-21 hand. This pays 3:2 if the player's two-card side 21 wins, and pays 1:2 on a two-card side tie.
I'll have to go over my code again - the 3.036% I get is supposed to include the half-unit bonus.
I am also assuming that it is a one-deck game - is this correct?